We develop tractable convex relaxations for rank-constrained quadratic optimization problems over nxm matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral structure. We derive lifted semidefinite relaxations that do not require such spectral terms. Although a direct lifting introduces a large semidefinite constraint in dimension n2 … Read more
This document briefly describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required. ArticleDownload View PDF
This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and Oh. The reconstruction is accomplished by minimizing the nuclear norm, or sum of the singular … Read more